Lunar Theory, Astronomia Vedica & Newton

In the West, the Lunar Theory, an explanation of the perturbations of the Moon based on the Law of Gravitation, is attributed to Newton. Newton was not only a star in Physics, but in Astronomy as well.

In the hoary books of Vedic Astronomy, the longitude of the Moon is computed based on the Lunar Theory. Moon's Parallactic Equation, Annual Equation, The Variaton, Evection etc are considered and 14 trignometric corrections are given to get the true sidereal longitude of Luna

Here are the calculations in Astronomia Vedica

The Perturbations of the Moon

(Ms - Mean Anomaly of the Sun; Mm - Mean Anomaly of the Moon; Ls - Mean Longitude of the Sun; Lm - Mean Longitude of the Moon; D = Lm - Ls ( Thidhi); Nm - Node of the Moon. These values are Sidereal or Nirayana )

14 Kendras are to be made and 14 trignometric corrections are to be given, according to astronomical savants. These 14 reductions are mandatory and only after these reductions can we get the true longitude of the Moon.

First Kendra
Sin ( Ms + 180 ) * 658
Second Kendra
Sin ( Lm - Ls ) * 121
Third Kendra
Sin ( 2*D - Mm ) * 4467
Fourth Kendra
Sin ( 2*D + 6 Signs ) * 2145
Fifth Kendra
Sin (( 2*D - Mm -Ms ) + 180)* 198
Sixth Kendra
Sin ( 2*D - Ms ) * 155
Seventh Kendra
Sin ( Mm- Ms + 180 ) *112
Eighth Kendra
Sin ( 2( Lm - Nm- Mm +180))* 85
Ninth Kendra
Sin ( 2*Ls - Nm ) * 81
Tenth Kendra
Sin ( Mm - Ms )* 73
Eleventh Kendra
Sin ( 2*D + Mm ) * 60
Twelfth Kendra
Sin ( 2*Mm - 2 D + 180 ) * 42
Thirteenth Kendra
Sin ( 4*D - Mm ) * 35
Fourteenth Kendra
Sin ( 4*D - 2*Mm +180)* 30

These trignometric corrections should be added to Moon's Mean Longitude if the Kendra is in the Southern Celestial Hemisphere and deducted if the Kendra is in the Northern Celestial Hemisphere and then we get the Samskrutha Chandra Madhyamam or the Cultured Mean Longitude of the Moon. Manda Kriya ( Reduction to True Anomaly ) must be done. Then Parinathi Kriya ( Reduction to Ecliptic ) should be done and what we get then is the longitude of the Moon along the Ecliptic !

Viskshepa Vrittopa Gatho VipathaThasmannayel Jyam Parinathyabhikhyam
Yugmaupada Swarnam Idam VidheyamSyath Kranti Vritteeya Ihaisha Chandra !

After the Reductions Fourteen,

Sin M to be added or minussed thereby
To the Cultured Longitude Mean;

The Node to be deducted &
Reduced to the Earth's Path ( Ecliptic );

thus shall we get as the resultant Value,

Luna's true Sidereal Longitude !